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Equation 5 · Part 7 · The Main Technical Approaches to AI Alignment, Compared

Symbol r_psi

PAI(yA≻yB∣x,C)=σ(rψ(x,yA,C)−rψ(x,yB,C)),P_{\mathrm{AI}}(y_A \succ y_B \mid x, C) = \sigma\big(r_\psi(x,y_A,C) - r_\psi(x,y_B,C)\big),
rψr_\psi

What this part means

rpr_psi is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

rpr_psi is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

Constitutional AI keeps RLHF’s reward-model-and-KL-penalty backbone intact and changes where the comparison labels come from. Bai and colleagues describe a two-phase method: a supervised phase in which the model critiques and revises its own responses against a written set of principles, and a reinforcement phase in which a model, rather than a human, judges which of two candidate responses better satisfies those principles — producing an AI-generated preference dataset that trains the reward model [ 6 ] . Formally, this changes only the source of the comparison label. The Bradley–Terry equation above is unchanged in form; what changes is that the probability being fitted is now [displayed…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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